PROCEDURE:
Part A:
1. Set the Hewlett-Packard multimeter as
an ohmmeter, and measure R1 and R2.
Set it as a voltmeter, and measure Vo
(from the terminals beside your sink)
and E (from the dry cell battery). Set up
the apparatus as in the figure to the
right.
E ~ 1.5 V
R1 ~ 470
I1
I2
Io
R2 ~ 100
Vo ~ 3.0 V
2. Calculate the current and the voltage for each resistor by using Kirchoff’s rules and Ohm’s
Law.
3. Measure the voltage across, and the current through each resistor. Record in the data table.
4. Compare the experimental and the calculated I and V values by computing the percent
difference.
Part B:
R1 ~ 100
1. Measure R1, R2, R3, R4 and Vo,
then set up the apparatus as in the
figure to the right.
I1
R2 ~ 330
I2
R4 ~ 470
R3 ~ 1000
I3
I4
Io
2. Repeat steps 2 to 4 of part A.
Vo ~ 3.0 V
Part C:
Io
1. Measure R1, R2, R3, and Vo,
then set up the apparatus as in
Vo ~ 3.0 V
the figure to the right:
I4
I1
R1 ~ 470
2. Repeat steps 2 to 4 of part A.
- 31 -
I2
R2 ~ 100
I3
R3 ~ 330
DATA:
Part A:
R1 = ____________
R2 = ____________
Vo = ____________
E = __________
Calculations using Kirchoff's rules:
Calculated
V1
(V)
V2
(V)
I1
(A)
I2
(A)
Part B:
Experimental
% difference
R1 = ____________
R2 = ____________
R3 = ____________
R4 = ____________
Vo = ____________
Calculations using Kirchoff's rules:
Calculated
V1
(V)
V2
(V)
V3
(V)
V4
(V)
I1
(A)
I2
(A)
I3
(A)
I4
(A)
Experimental
% difference
- 32 -
Part C:
R1 = __________ R2 = __________ R3 = __________ Vo = __________
Calculations using Kirchoff's rules:
Calculated
V1
(V)
V2
(V)
V3
(V)
I1
(A)
I2
(A)
I3
(A)
Experimental
% difference
- 33 -
Experiment 10: MAPPING THE MAGNETIC FIELD
PURPOSE: a) To determine the shape of magnetic fields around magnetic poles.
b) To map the magnetic field around a bar magnet.
c) To determine the strength of the north pole of a bar magnet.
INTRODUCTION:
1. Each pole of a bar magnet placed in an external uniform magnetic field B experiences a
force F proportional to the magnitude of the field.
F
N
B
The magnetic pole strength m of a magnetic pole is the ratio between the force and the external
magnetic field;
F
m=
,
or
F = mB .
B
2. At moderate distances from a magnetic pole, its magnetic field can be approximated as
pointed radially outward (for a north pole) or inward (for a south pole), with a magnitude of
B=
km  m
r2
where the constant km = 10-7 Tm/A.
3. If a pole of one magnet of magnetic pole strength m 1 is placed at a moderate distance r from a
pole of another magnet of magnetic pole strength m 2, each pole will lie in the other pole’s
magnetic field, and will experience a force
F=
k m  m1m 2
.
r2
This behavior is analogous to Coulomb’s law for electricity.
APPARATUS:
Large plywood board
2 bar magnets
Protractor
Magnetic compass
22" X 34" paper
8 ½ " X 11" paper
- 34 -
2 horseshoe magnets
Iron filings
Plexiglas sheet
PROCEDURE:
PART A: THE SHAPE OF THE MAGNETIC FIELD
1. Clear your table of all objects, then place two bar magnets on your table, lined up horizontally
North pole to North pole, 5 centimeters apart.
2. Place the 8 ½ " X 11" paper on top of the Plexiglas sheet placed above the magnets, then
gently sprinkle a very thin layer of iron filings over the paper. Be careful not to spray iron filings
onto the table or the floor.
3. Tap the edges of the paper lightly until the field lines gradually show up, and sketch the results
on the back of the last page of the lab. When finished, return the iron filings to the container
that they came from. Try not to spill the filings, as they are difficult to clean up.
4. Repeat steps 1 - 3 with the three other pole arrangements shown below.
N
5 cm
S
N
N
S
S
N
S
S
N
Fig. 1.
PART B: MAGNETIC FIELD LINES
1. Place the 22" X 34" paper on the
plywood board suspended between
two tables. Place a compass at the
center of the paper (as far as possible
from the metal bars that run beneath
the tables), and align one edge of the
paper parallel to the Earth’s magnetic
field. Tape a magnet to the middle of
the edge of the paper with the North
pole of the magnet pointing toward
magnetic North.
Magnetic
North
N
A
A
S
2. Draw the line AA, pointed towards
the center of the magnet, as shown in
Fig. 2. Draw lines BB and CC about
5 cm from each edge parallel to line
AA.
Fig. 2
- 35 -
3. Starting on line AA 10 cm away from the bar magnet, mark the position of the tip and tail of the
compass needle.
4. Move the tail of the needle to coincide with the tip of the previous compass position. Continue
the process in both directions until the field line terminates at a pole of the magnet or at the
edge of the paper.
5. Join the dots which mark the changing positions of the compass needle tip with a smooth line.
Repeat this process for positions of 20, 30, 40, 50 and 60 cm from the magnet.
6. Repeat steps 3 – 5 along line BB and CC.
PART C: MAGNETIC POLE STRENGTH (m)
1. At point A the magnetic field of the Earth
dominates, and the compass points
towards magnetic North. At point A the
magnetic field of the bar magnet
dominates, and the compass points in the
opposite direction. At some point along
the line AA the two fields cancel, as
shown in Figure 3, and the compass points
aimlessly when it is shaken. Use the
compass to find this neutral point, and
label it.
Magnetic
North
BE
r
N

A
S
A
BN
BS
Bmagnet
Fig. 3.
2. For Harbor College, the horizontal component of the Earth’s magnetic field is BE = 2.50 X 10-5
Teslas. The neutral point is a moderate distance from the bar magnet, so the bar magnet may
be considered as a magnetic dipole, with each pole contributing a magnetic field BN and BS at
the neutral point. Assuming the poles have equal magnetic pole strengths, B N sin = ½ BE.
Calculate BN, and the magnetic pole strength m of the bar magnet.
DATA:
 = ___________________
BN = ___________________
r = ___________________
m = ___________________
- 36 -
Experiment 11: THE TANGENT GALVANOMETER
PURPOSE: To determine the horizontal component of the Earth's magnetic field.
INTRODUCTION:
N
BH is the horizontal component of the Earth’s
magnetic field.
The tangent galvanometer’s
compass needle points in this direction when no
electricity is supplied to the galvanometer, as shown
in Figure 1.
Bi is the magnetic field created by the current i
through the galvanometer.
E
W
S
BH

B is the vector sum of BH and Bi. The compass
needle points in this direction when the current i
flows through the tangent galvanometer.
B
Bi
Fig. 1
5
Turns
10
Turns
15 Turns
Tangent Galvanometer
Magnetic Field and Current
Bi may be found from Bi = Noi / 2R, where
Binding Posts Configuration
N = # of turns
o = 4 X 10-7 N / A2
i = current
R = Radius of coil
Once  and Bi are known, BH may be calculated from BH = Bi / tan .
APPARATUS:
Tangent galvanometer
DC power supply
Hewlett Packard multimeter
6 spade lugs
20-rheostat
DPDT reversing switch
Metric ruler
Transfer calipers
- 37 -
Plywood board
Circular bubble level
7 patch cords
PROCEDURE:
G
1. Set the multimeter dial to 10A, and use the
Fused and Common terminals. Set the power
supply to 5V.
Set up the apparatus as in Figure 2, using the
5-turns posts with the switch open (raised).
The tangent galvanometer should be set on a
plywood board between two tables, to
minimize the magnetic deflection due to the
metal support rod that runs along the
underside of each table.
A
Reversing
Switch
Rheostat
-
+
5V
Fig. 2.
2. Set the rheostat to minimum voltage (and minimum current) by sliding the contact to the
negative terminal.
3. Use the transfer calipers and the metric ruler to measure the diameter of the tangent
galvanometer’s coil to the nearest millimeter. Divide by two to get the coil radius R, and
place on the data sheet.
With the switch still open, rotate the galvanometer so the short, blue-and-silver compass
needle is parallel to the loops of wire (coil), as seen from above. Place the circular bubble
level on the base of the tangent galvanometer, and adjust the height of the feet until the
galvanometer is level. Rotate the compass dial until the long needle (perpendicular to the
compass needle) reads 0o.
4. Close the switch and deflect the compass needle clockwise 45 o by adjusting the rheostat,
and record the absolute value of the current icw. Close the switch on the other side and
deflect the compass needle counter-clockwise 45o by adjusting the rheostat, and record the
absolute value of the current iccw.
5. Calculate iaverage. Calculate Bi and BH, and convert them to microteslas (1 T = 10-6 T).
6. Repeat steps 4 and 5 for a 60o deflection.
7. Repeat steps 4 to 6 using the terminals on either side of the ‘10’ on the tangent
galvanometer. This means that the current runs through N = 10 loops of wire.
8. Repeat steps 4 to 6 using the left and right terminals, so N = 15. Leave the switch open
when finished.
9. Calculate an average value of B from these six measurements, and calculate its standard
deviation and standard error, with n = 6.
10. Calculate the percent difference between your value of B H and the accepted value,
BH = 25.0 T.
- 38 -
DATA:
Radius of Coil = ____________ m
BH Earth estimated value between 0.2 G to 0.25 G. (1 G = 10-4 T)
BH (calculated) = Bi / tan 
Angle of
Deflection
Bi = Noi / 2R
N = # of turns in coil
N
45o
5
60o
5
45o
10
60o
10
45o
15
60o
15
iCW
iCCW
iAverage
Bi
BH
Calculated
(A)
(A)
(A)
(T)
(T)
Standard deviation =  =
B
H
Average
(T)
Deviation
From
Average
(BH - B H )
(T)
_________
 (B H  B H ) 2
= ________________ T
n 1
Horizontal component of the
Earth's magnetic field at this location
= ________________ T ± ________________ T
Average value ± standard deviation
where n = the number of BH values.
- 39 -
Experiment 12: AC - RL , AC - RC CIRCUITS
PURPOSE:
To study the role of an inductance coil (inductor) in an AC series circuit. (Low pass filter).
To study the role of a capacitor in an AC series circuit. (High pass filter).
INTRODUCTION:
AC power supply:
Input
__________ Volts (Vs) __________ Hz (f)

R
Output
Vs 
I
R
VR
I = VR/R
With inductor:
L
L
Vs 
I
R
Input
VR
XL = 2fL (Theory)
VL =
Vs2

Output
XL = VL/I
Vs
2
VR
VL
VR
L
Vs

VR
Fig. 1.
- 40 -
With capacitor:
C
C
Vs 
I
XC = 1
2fC
R
Input
VR
(Theory)
Output
XC = VC/I
Vs
VC =
Vs2

VR2
VC
VR
C

Vs
VR
Fig. 2.
APPARATUS:
Function generator
Ruler and French curve
Leads & connectors
Inductor L = 10 mH
Resistor, composition: 470 
Decade capacitor box (C = 0.5F)
BNC to banana adaptors
Digital voltmeter
Breadboard
Frequency counter
PROCEDURE:
PART A: INDUCTIVE REACTANCE
1. Set up apparatus as in Figure 1.
2. Set the function generator (Vs) at 3 Vrms and 1000 Hz.
3. Record Vs and VR in data table.
4. Determine
VL from VL = Vs2  VR2
I from I = VR / R
XL from XL = VL / I
5. Repeat steps 2 through 4 for f = 1500 Hz to 4500 Hz in steps of 500 Hz.
6. Plot XL versus f.
7. Plot I versus f.
- 41 -
Part B, Capacitive reactance
1. Set up apparatus as in Figure 2.
2. Set function generator at 3 Vrms and 1000 Hz.
3. Record Vs and VR on data table.
4. Determine
VC from VC = Vs2

VR2
I from I = VR / R
XC from XC = VC / I
5. Repeat steps 2 through 4 for f = 1000 Hz to 4500 Hz in steps of 500 Hz.
6. Plot XC versus f.
7. Plot I versus f.
- 42 -
DATA
Data Table 1, Inductive Reactance
Frequency
f
(Hz)
Source
Voltage Vs
(V)
Voltage
Across
Resistor VR
(V)
Voltage
Across
Inductor VL
(V)
Current I
(A)
Inductive
Reactance
XL
Theoretical
XL
()
()
1500
2000
2500
3000
3500
4000
4500
CALCULATIONS:
GRAPHS:
I (A)
XL
)
f (Hz)
f (Hz)
- 43 -
% difference
Data Table 2, Capacitive Reactance
Frequency
f
(Hz)
Source
Voltage Vs
(V)
Voltage
Across
Resistor VR
(V)
Voltage
Across
Capacitor VC
(V)
Current I
(A)
Capacitive
Reactance
XL
Theoretical
XC
()
()
1000
1500
2000
2500
3000
3500
4000
4500
CALCULATIONS:
GRAPHS:
I (A)
XC
)
f (Hz)
f (Hz)
- 44 -
% difference
Experiment 13: AC - RLC CIRCUIT
PURPOSE
a) To determine the resonance frequency f o
b) To determine the bandwidth | f2 - f1 |
fo
c) To determine the quality Q =
of this AC - RLC circuit.
| f 2  f1 |
INTRODUCTION: In an AC-RLC circuit:
L
C
~
L
R
C
R
Input Vs
Output VR
At the resonant frequency: XL = XC
2foL =

Vs
V
= R
Z min
R
At resonance: I max =
At all f: I =
1
2f o C
fo =
1
2 LC
where Z =
R 2  ( XL  X C ) 2
VR
Z
I
Imax
Small R
0.707 Imax
Bandwidth = | f2 - f1 |
Larger R
Quality Factor Q =
f1 fo f2
fo
| f 2  f1 |
f
APPARATUS:
Inductor L = 10 mH
Carbon resistor 10  and 100 
Function generator (AC power supply)
Breadboard and wires
Digital voltmeter
Decade capacitor box
Dual trace oscilloscope
Coaxial cable
Ruler and French curve
Frequency counter
- 45 -
PROCEDURE:
PART A:
L
C
1. Set up the apparatus as in Figure 1.
2. Calculate fo from the values of
capacitance and inductance. Use
R = 10 .
R
~
Frequency
Counter
3. Maintain Vs at 0.40 V peak to peak
by monitoring channel A of the
oscilloscope.
Oscilloscope
4. Starting with fo, take voltage
readings at +500-Hz intervals up to
f = fo + 2000 Hz.
Ch. A
Ch. B
Fig. 1
5. Starting with fo, take voltage readings at 500-Hz intervals up to f = fo  2000 Hz.
6. Record the voltages in data in table A.
recorded voltages.
Calculate the corresponding current from the
7. Plot Irms vs. f and P vs. f.
8. Determine the bandwidth and quality of the circuit from graphs (at I = 0.707 Io and at P =
½ Po, the half power point).
9. Determine fo from the graph and compare with the calculated value.
10. Repeat steps 1 through 9 for R = 100 .
PART B: SCANNING
L
1. Connect
the
oscilloscope
across R. See
Figure 2.
C
Oscilloscope
Frequency
Counter
~
R
Ch. A
Fig. 2.
2. Sweep across frequency range 1000 to 10,000 Hz.
3. Notice the change in amplitude of AC signal on scope. As the frequency goes above and
below the resonance frequency fo, the source voltage varies. To maintain a constant source
voltage, step 3 of Part A is essential.
- 46 -
DATA FOR PART A:
R = __________
L = __________
1
fo =
= __________
2 LC
C = __________
Data Table A:
Source
Frequency f
(Hz)
I
f Steps
(Hz)
Imax
fo - 2000
0.707 Imax
fo - 1500
fo - 1000
fo - 500
f1 fo f2
f
fo - 250
(Close to)
fo
P
fo + 150
Po
fo + 300
fo + 500
1/2 Po
fo + 1000
fo + 1500
f1
f2
f
fo + 2000
Experimental values from graph:
f1 = ________________ Hz
f2 = ________________ Hz
Resonance frequency = fo = ________________ Hz
Experimental Bandwidth = f2  f1 = ________________ Hz
fo
Experimental Quality =
= ________________
f 2  f1
- 47 -
Vo
(V)
Irms
(A)
Paverage =
(Irms)2R
(W)
DATA FOR PART B:
R = __________
L = __________
1
fo =
= __________
2 LC
C = __________
Data Table A:
Source
Frequency f
(Hz)
I
f Steps
(Hz)
Imax
fo - 2000
0.707 Imax
fo - 1500
fo - 1000
fo - 500
f1 fo f2
f
fo - 250
(Close to)
fo
P
fo + 150
Po
fo + 300
fo + 500
1/2 Po
fo + 1000
fo + 1500
f1
f2
f
fo + 2000
Experimental values from graph:
f1 = ________________ Hz
f2 = ________________ Hz
Resonance frequency = fo = ________________ Hz
Experimental Bandwidth = f2  f1 = ________________ Hz
fo
Experimental Quality =
= ________________
f 2  f1
- 48 -
Vo
(V)
Irms
(A)
Paverage =
(Irms)2R
(W)
Experiment 14: THE VISIBLE SPECTRUM
PURPOSE:
The wavelengths of electromagnetic waves in the visible range will be determined with a
diffraction grating.
INTRODUCTION:
A diffraction grating consists of a number of closely-spaced parallel grooves ruled on a
transparent surface. It is a useful device for dispersing the waves of different wavelength in a
source of light. The effect of a grating is similar to a prism but exhibits greater resolving power.
The two dots in Figure 1 represent adjacent grooves on a diffraction grating, a distance d
apart. When the two rays of light entering from the left strike the two grooves, each ray is
scattered in all directions. A bright spot will appear on a distant screen if the two scattered rays
heading toward the lower right are in phase, so that constructive interference occurs. As may be
seen in Figure 1,  is the difference in the path lengths of the two scattered rays of wavelength .
The two rays will be in phase if  = 0 or 1 or 2 for example. Call n = 0, 1, 2… the order of the
diffraction. Then constructive interference occurs if  = n. From the geometry of Figure 1,
 = d sin. Equating these two, n = d sin, so =
Laser Light

d sin 
.
n
L
Laser Light

d

Laser Light
x
Grating
Grating
Screen
Fig. 1.
Fig. 2.
APPARATUS:
Power supply for lamp, 12V
Helium-neon laser
(2) one-meter sticks
Large replica grating
Large piece of cardboard
Laboratory jack
White light source
Two-meter stick
Grating stand & holder
Darkened room
- 49 -
(4) Buret clamps
Ledger paper
Masking tape
(2) Ring stands
PROCEDURE:
PART A: DETERMINATION OF THE GROOVE SEPARATION d
1. To determine the diffraction
grating spacing d, set up the
grating and helium-neon laser as
shown in Figure 3.
Set the
grating at exactly L = 2.000 m
from the blackboard. Orient the
grating perpendicular to the
beam. Measure the distance x
for the orders n = 1 and n = 2.
Calculate tan  = x/L, as shown
in Figure 2.
Determine an
average value for the grating
groove spacing d from your data.
The wavelength of the laser light
is 633 nm.
xleft
0center
L

He-Ne Laser
xright
Lab Jack
Fig. 3
PART B: DETERMINATION OF THE WAVELENGTH RANGES FOR VISIBLE LIGHT
1. Set up the apparatus as shown in Figure 4, replacing the laser with a white light source. The
white paper can be taped to a piece of cardboard suspended vertically between the two ring
stands on one table, and the white light source and diffraction grating can be placed on the
table behind it. Adjust the lens or the filament position to create a sharp image of the filament.
2. Record L. Record x for the boundary between each color.
0th order
White
White-light source
Violet
Blue
Green
Yellow
Orange
Red
xupper (Violet)
xlower (Violet) = xupper (Blue)
Fig. 4.
3. Calculate , and calculate the percent difference between your results and the (rather
arbitrary) values given below.
Color
Violet
Blue
Yellow
Green
Orange
Red
upper
400 nm
424 nm
491 nm
575 nm
585 nm
647 nm
- 50 -
lower
424 nm
491 nm
575 nm
585 nm
647 nm
700 nm
DATA:
Data Table A: Distance L from grating to screen = 2.000 m
Wavelength
| xright|
(m)
n
| xleft|
(m)
tan 
xaverage
(m)

sin 
d
n
sin 
1
633 nm
2
Average value of d = ________________ nm
Data Table B: L = _____________ m
Color
x
(m)
tan 
n = 1, so  = d sin 

sin 

(nm)
xu
u
xl
xu
l
xl
xu
l
Green
xl
xu
l
Yellow
xl
xu
l
xl
xu
l
xl
l
Violet
Blue
Orange
Red
u
u
u
u
u
- 51 -
% difference
Experiment 15: REFLECTION & REFRACTION
PURPOSE: To show by means of ray tracing:
a) The angle of incidence, i equals the angle of refraction, r.
b) The virtual image is the perceived location of the object behind the mirror.
c) The deflection angle, d is twice the angle through which a mirror is rotated.
d) The index of refraction can be determined using Snell's law.
INTRODUCTION:
All electromagnetic (em) waves exhibit similar wave properties. In this
experiment, em waves in the visible region, light waves, will be used to illustrate some of these
wave properties.
Electromagnetic Spectrum
Wave Properties
Long 
Short 
RADIO UHF VHF
IR VIS UV
X-RAYS
1.
2.
3.
4.
5.
-RAYS
Light 700 nm  400 nm
Reflection
Refraction
Diffraction
Interference
Polarization
Refraction
Reflection
i
i
n1
r
n2
r
Reflection of waves (ray)
Transmission of waves (ray) with a change
 1 =  2
in velocity. n1 sin 1 = n2 sin 2
(Snell's Law)
q
APPARATUS:
Pins & cork board
Plastic triangle
Plane mirror
Colored pencils
Pencil compass
Refraction cube
Ledger paper
Ruler
Refraction plate
PROCEDURE:
PART A: VIRTUAL IMAGE IN PLANE MIRROR
1. Support the mirror as shown in figure 1. Draw a
line along the back of the mirror and a triangle in
front of it.
A
C
L2
2. Place a pin at A as shown in Figure 1.
L1
3. Place a pin at R1, about 10 to 15 cm to the right
of the triangle.
- 52 -
A
R2
R1 B
Fig. 1.
4. View R1 from behind and place R2 so that R1, R2,
and A appear in a straight line. Repeat steps 3
and 4 from the left side with pins L1 and L2. See
Figure 2.
A
P
5. Draw R1R2 and L1L2 to the mirror.
R2
L2
6. Remove the mirror. Extend this line dashed
behind mirror until R1R2 and L1L2 meet at A.
Remove pin A and repeat steps 3 – 5 for pins at B
and C. See Figure 1b.
R1
A
L1
7. Join points A, B and C to reconstruct the image.
8. Fold the paper on the mirror line. What can you
say about the mirror image of the triangle?
Fig. 2
PART B: ANGLE OF INCIDENCE AND ANGLE OF REFLECTION
1. Join points A and P as shown in Figure 3.
A
Pin Image
P
2. Draw a line perpendicular to the mirror
surface at P.
R2
3. Measure the angle of incidence, i , and the
angle of reflection, r.
A
i
r
R1
Object
PART C: ROTATION OF MIRROR
1. Set up mirror as in Figure 4 with pins at A and B. Draw line AB to mirror surface at P.
A
A
Pivot Point
B

B
Mirror
P
Initial Mirror position
B

C
Rotation angle
Final Mirror position
A
E

D
Initial reflected ray
Incident ray
Final reflected ray
F
Fig. 4.
- 53 -
2. Draw the mirror line (reflecting surface) and mark point P.
3. Draw line CD by aligning pins C and D so C, D, A and B appear on a single line.
4. Leave A and B in place. Rotate the mirror 8 - 10 degrees clockwise with P as the fixed pivot
point with the axis of rotation through P. Then, looking into the mirror, line up pins E and F so
that E, F, A and B' appear on the same line.
5. Measure the angle between the reflected rays CD and EF. The angle , is the angle of
deflection of the reflected ray.
6. For a mirror rotation of 10o, how much has the reflected beam been rotated?
PART D: INDEX OF REFRACTION
1. Place a glass cube on paper and trace the
outline of the cube.
2. Draw a normal to the surface at R and lines
AR, BR and CR at 15, 30 and 45 degrees to
the normal respectively.
3. Place pins at R, A, B, and C as indicated in
figure 4.
15o A
i
n1
Medium 1, air
C
R
Medium 2, glass
n2
4. View A and R through glass cube and place
pin A' on the edge of the plate so that A', R
and A all appear on a straight line.
r
C
5. Repeat for pins B and C.
B
B
A
Normal
6. Remove the glass cube and join points R
and A', R and B', and R and C'.
7. Measure iA ____________iB ____________iC ____________
rA ____________rB ____________rC ____________
8. Calculate n, the index of refraction of the glass (n = sini / sinr) using the angles of refraction
for the rays AR, BR and CR.
c
9. Calculate the velocity of light through glass v = n .
- 54 -
Experiment 16: THE THIN LENS
PURPOSE: a)
b)
c)
d)
To measure the focal length of thin lenses.
To observe characteristics of images formed.
To verify the lens equation.
To practice drawing ray diagrams.
INTRODUCTION:
Thin lenses:
Biconvex lens (converging) f + ;
Biconcave lens (diverging) f -
Ray diagrams--See ray diagram charts.
Object
Object
F
F
Real
image
F
Concave lens
Convex lens
Lens Equation:
1
so
 1  1
s
F
Virtual
Image
f
so = object to lens distance
s = image to lens distance
f = focus F to lens distance (focal length)
APPARATUS:
Optical bench and accessories
Screen
Diopter gauge
Light source (object)
Lenses
Meter stick
Dark room
Gooseneck lamp
PROCEDURE:
Part A: FOCAL LENGTH OF BICONVEX LENS
1. Set up the apparatus as in Figure 1.
s
2. Slide screen back and forth to focus the
image of a distant object onto the screen.
Fig. 1
3. Measure the image distance s. This is equal to the focal length of the lens since the first term
in the lens equation goes to zero. Write down this result on the top of Table 1.
- 55 -
PART B: VERIFYING THE LENS EQUATION EXPERIMENTALLY AND WITH RAY DIAGRAMS
1. Set up the apparatus as in Figure 2.
2. Place the object at the following positions:
a. so > 2f
b. so at 2f
c. f < so < 2f
d. so = f
e. so < f
so
s
Fig. 2
3. Record so and s in Table 1. Calculate f using the lens equation. Determine the magnification
M =  s/so and describe the image. For positions d and e, s cannot be measured, but can be
calculated by using the value of f from part A.
4. Draw ray diagrams to scale for each case on graph paper.
PART C: FOCAL LENGTH OF BICONCAVE LENS
1. Remove the metal cover from the top of the diopter gauge. Place the central prong against the
middle of one side of the lens, and record the reading on the outer (red) scale. Repeat with
the other side of the lens. Add these two numbers. The inverse of the sum is the approximate
focal length (as a negative number) in meters. Write down this result on the top of Table 2,
and recap the diopter gauge.
PART D: OBSERVATION OF IMAGES PREDICTED WITH LENS EQUATION
Lens Equation:
1
so
 1  1
s
f
1. Set up apparatus as in Figure 3.
2. Repeat step 2 of part B, recording so for
each position.
Calculate the object
distance s by using the value of f from
part C.
Determine the magnification
M = s/so and describe the image.
F
F
Eye
Fig. 3
3. For each of the five positions, place the meter stick vertically at the calculated image distance,
and note that the image (seen through the lens) appears to be at the same distance as the
meter stick (not viewed through the lens).
4. Draw ray diagrams to scale.
- 56 -
DATA:
Data Table 1: Convex lens
Object Position
so
(cm)
s
(cm)
f
f = _____________ (measured in Part A)
so > 2f
(Ray Diagram a)
so = 2f
(Ray Diagram b)
f < so < 2f
(Ray Diagram c)
so = f
(Ray Diagram d)
so < f
(Ray Diagram e)
(measured)
(measured)
(measured)
(calculated)
(calculated)
(calculated)
(calculated)
(calculated)
(measured)
(measured)
(cm)
M
Real or Virtual
Upright or Inverted
Enlarged or Smaller
RAY DIAGRAMS:
a.
c.
. .F
b.
. .
d.
F
Virtual Image
e.
.
- 57 -
.F
. .
F
..
F
No Image
Data Table 2: Concave lens.
Object Position
so > 2f
(Ray Diagram a)
so
(cm)
s
(calculated)
(cm)
f
(measured)
(cm)
f = _____________ (measured)
so = 2f
(Ray Diagram b)
f < so < 2f
(Ray Diagram c)
so = f
(Ray Diagram d)
M
Real or Virtual
Upright or Inverted
Enlarged or Smaller
RAY DIAGRAMS:
a.
. .F
b.
c.
. F.
d.
. .
F
e.
. .F
- 58 -
. .F
so < f
(Ray Diagram e)